Rank Of bicomplex matrices and system of algebraic equations

TL;DR

This paper investigates the rank properties of bicomplex matrices and introduces a new technique for solving systems of algebraic equations in bicomplex space, establishing conditions for solution existence.

Contribution

It provides a novel approach to solving bicomplex systems and clarifies the relationship between different rank concepts in bicomplex matrices.

Findings

Established a necessary and sufficient condition for solution existence

Analyzed the relationship between rank, idempotent column rank, and row rank

Presented a new technique for solving bicomplex algebraic systems

Abstract

In this paper, we study the rank of matrices of bicomplex numbers. The relationship between rank, idempotent column rank and idempotent row rank is examined. Then, the solution of a system of equations in bicomplex space is presented using a new technique. Moreover, we establish a necessary and sufficient condition for the existence of solutions of a system of equations in bicomplex space and derive some related results.